Ω-RESULT ON COEFFICIENTS OF AUTOMORPHIC L-FUNCTIONS OVER SPARSE SEQUENCES

Title & Authors
Ω-RESULT ON COEFFICIENTS OF AUTOMORPHIC L-FUNCTIONS OVER SPARSE SEQUENCES
LAO, HUIXUE; WEI, HONGBIN;

Abstract
Let $\small{{\lambda}_f(n)}$ denote the n-th normalized Fourier coefficient of a primitive holomorphic form f for the full modular group $\small{{\Gamma}=SL_2({\mathbb{Z}})}$. In this paper, we are concerned with $\small{{\Omega}}$-result on the summatory function $\small{{\sum}_{n{\leqslant}x}{\lambda}^2_f(n^2)}$, and establish the following result $\small{{\sum}_{\leqslant}{\lambda}^2_f(n^2)=c_1x+{\Omega}(x^{}$$\small{\frac{4}{9}})}$, where $\small{c_1}$ is a suitable constant.
Keywords
automorphic L-functions;holomorphic cusp forms;Omega theorem;
Language
English
Cited by
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